A benchmark problem in active aerodynamic flow control, suppression of pressure oscillations induced by flow over a shallow cavity, is used in this paper to present a comprehensive approach to reduced-order model based flow control. Proper orthogonal decomposition and Galerkin projection techniques are used to obtain a reduced-order model of the flow dynamics from experimental data. The model is made amenable to control design by means of a control separation technique. Quadratic stochastic estimation is used to correlate flow field data with surface pressure measurements to reconstruct the state of the model in real time. Experimental results show that a linear-quadratic controller designed on the basis of the reduced-order model achieves a significant attenuation of the resonant tone with a redistribution of the energy into other frequencies, and exhibits a certain degree of robustness when operating in off-design conditions.